Theorem nfcri

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by Gino Giotto, 23-May-2024) Avoid ax-12 (adopting Wolf Lammen's 13-May-2023 proof). (Revised by SN, 3-Jun-2024)

	Ref	Expression
Hypothesis	nfcri.1	|- F/_ x A
Assertion	nfcri	|- F/ x y e. A

Proof

Step	Hyp	Ref	Expression
1		nfcri.1	|- F/_ x A
2		nfcr	|- ( F/_ x A -> F/ x y e. A )
3	1 2	ax-mp	|- F/ x y e. A